To transform a digital image to a finished print of high quality requires that noise components, introduced because of the transformation of the image from the original scene to electrical signals, be reduced and/or eliminated such that the noise does not become discernible to the human eye.
One of the methods receiving widespread use in the prior art is related to smoothing the differences between the values of the gray levels of pixels located in neighborhoods. A difficulty associated with this smoothing process is that it not only removes the noise components, but it also blurs the edge values. The edges exist when there is a transition region such as a region containing sharp detail, for example grass, which may define or outline a neighboring region which may be either smooth or sharply detailed.
A patent of interest for its teaching of noise reduction in a data processed image is U.S. Pat. No. 4,734,770 entitled, "Image Data Processing Method and Device Therefor" by I. Matsuba. The method of that patent treats the first image data set, consisting of a plurality of pixels having values corresponding to their gray level, some of which contain noise components, by transforming them into second image data to reduce the noise components appearing in the second image data. The method operates by selecting pixels to be treated and obtaining proposed values (candidate values) which should be given to the object pixels based on the stated relationship. A probability function is used to determine whether a pixel in question should be raised to the candidate value or be maintained at its present value. The probability formula includes the image energy component as one of its items. A recognition is made for edges of patterns based on the energy level comparisons, wherein a high energy level difference between a central and an adjoining pixel would have a high probability of defining an edge.
In the cross-referenced related applications a solution to the edge blurring, when performing the smoothing operation, approaches the problem by determining edge regions and by leaving those regions undisturbed or unoperated upon and by applying a smoothing function to the smooth regions so as to reduce noise in those areas. The aforementioned solution has two responsibilities, number one to identify whether a pixel belongs to an edge or to a smooth region and, number two, to compute a smoothing code value for the pixel if it belongs to a smooth region. These two operations are called "segmentation" and "smoothing", respectively. Both of the aforementioned tasks are accomplished by a least squares fit of a plane to the image, in a neighborhood around the pixel of interest. If the goodness of the fit is small, then in that neighborhood the image is well approximated by a plane and thus must be a smooth region. Further, the fit provides a smooth estimate for the code value at the pixel of interest, which is the value of the fitted plane at the pixel of interest.
The methods of the cross-related applications perform their functions quite well. One area of improvement in the utilization of these methods is a reduction in the time of computation required for the least squares fitting and estimation of the fitted values. The present invention is directed to an efficient and quick method to compute the fit parameters and the fitted values in a pipeline manner based on the recursive nature of the computation.